According to wave theory, wave means not only vibration but also propagation of the vibration. To be specific, 1. vibration can be decomposed into translational vibration, rotational vibration; 2. wave field divergence drives pressure wave, and wave field curl drives shear wave; 3. translational vibration is a combined action of divergence and curl, including not only pressure wave but also shear wave; 4. rotational vibration is related only to curl; 5. volume curl is complete curl, and surface curl is incomplete curl. Accordingly, a technology that can only detect translational vibration cannot completely separate pressure wave from shear wave. Only a technology that can detect volume curl or divergence can work out pure shear wave and pure pressure wave.
Spatial motion properties of wave include abundant information, which play important roles in aspects such as wave field separation, signal-to-noise ratio, fidelity, imaging precision, medium attribute analysis, or the like. However, the existing acquisition technology can only detect information such as amplitude, frequency, phase or the like, and could not detect the spatial properties of wave motions.
Currently, detection of seismic wave is realized by converting wave vibration into an electric signal (voltage, current) or then converting the electric signal into a digital signal. A method of converting mechanical motion into an electric signal applies nothing more than an electromagnetic detector, a capacitance detector, a piezoelectric detector and a fiber optic strain detector.
The electromagnetic detector and the capacitance detector are of line-vibration type and have working direction. Ideal direction filtering effect is cos θ, out(t)=A(t)cos θ. A(t) and θ are both unknown, only a single device cannot work out the true amplitude A(t) and the angle θ. An MEMS detector basically belongs to a capacitance detector, which also follows the above rule.
The fiber optic strain detector may be line-vibration or pressure-intensity type, and only a single device cannot determine vibration direction either. Accordingly, a single electromagnetic detector, a single capacitance detector or a single fiber optic strain detector cannot distinguish wave field vibration direction, even not having the function of detecting wave field divergence or curl.
The piezoelectric detector is of pressure-intensity type, and the output is related to pressure intensity of surrounding liquid medium, which is non-directional and cannot distinguish vibration direction. Pressure intensity in a liquid environment is isotropic and is equivalent to wave field divergence. But in a terrestrial solid environment, even if the detector is put in a liquid container, the detector still fails to realize divergence measurement.
A three component detector can work out wave field vibration direction θ and amplitude A(t) by a three-vector combination method. This is also the reason why the three component detector is called a vector detector, but it only measure translational vibration vector of a point, cannot detect nature, curl and divergence of vibration.
In conclusion, various wave detectors in the prior art cannot realize detection of full information of the seismic wave field.
FIG. 1 is a schematic diagram of directional response of an ideal single wave detector in a pressure wave field in related art, and FIG. 2 is a schematic diagram of directional response of the ideal single wave detector in a shear wave field in related art, for describing operating directivity of the wave detector. As shown in FIGS. 1 and 2, the output of a wave detector is realized based on the formula: out=A·n=a×b cos θ. Wherein, A denotes wave field function and vector; n denotes a unit vector of the wave detector in the operating directivity; a denotes instantaneous amplitude of a wave field A in a vibration direction; b denotes sensitivity of the wave detector; θ denotes an angle between the operating direction of the wave detector and the vibration direction of the wave field at position of the wave detector; p denotes a pressure wave subscript; S denotes a shear wave subscript.
Specifically as shown in FIG. 1, the output of a wave detector in the pressure wave field is realized based on the following formula:
out=% Ap·n=ap×b cos θp; wherein, Ap denotes an isochronous surface of the pressure wave field; ap denotes an instantaneous displacement of the wave field Ap in a normal direction at the position of the wave detector; b denotes sensitivity of the wave detector; θp denotes an angle between the operating direction of the wave detector and the vibration direction of the wave field.
As shown in FIG. 2, the output of a wave detector in the shear wave field is realized based on the following formula:
out=As·n=as×b cos θs; wherein, As denotes an isochronous surface of the shear wave field; as denotes an instantaneous displacement of the wave field As in a vibration vector direction at the position of the wave detector; b denotes sensitivity of the wave detector; θs denotes an angle between the operating direction of the wave detector and the vibration direction of the wave field.
FIGS. 1 and 2 and the above formulas do not include other specification of an electromagnetic capacitance wave detector, only include directional description. The above formulas are only used for describing a single wave detector, which satisfies directional requirement of multi-dimensional space structure.
Seismic wave detection flow in traditional technology is as below:
Based on a wave equation, medium mass points satisfy the following movement relationship as in equation (1):
                              ρ          ⁢                                                    ∂                2                            ⁢                              U                →                                                    ∂                              t                2                                                    =                                            (                              λ                +                μ                            )                        ⁢            grad            ⁢                                                  ⁢            θ                    +                      μ            ⁢                                          ∇                2                            ⁢                              U                →                                              +                      ρ            ⁢                                                  ⁢                          F              →                                                          (        1        )            wherein, λ, μ denote Lamé constants, ρ denotes density, U denotes displacement vector, and t denotes time.
{right arrow over (F)} denotes an external force vector, {right arrow over (F)}=fx{right arrow over (i)}+fy{right arrow over (j)}+fz{right arrow over (k)}.
∇2 denotes Laplace operator,
      ∇    2    ⁢      =                            ∂          2                          ∂                      x            2                              +                        ∂          2                          ∂                      y            2                              +                                    ∂            2                                ∂                          z              2                                      .            
θ denotes a volumetric coefficient,
  θ  =            div      ⁢                          ⁢              U        →              =                            ∂          u                          ∂          x                    +                        ∂          v                          ∂          y                    +                                    ∂            w                                ∂            z                          .            
Solving divergence from the equation (1), to obtain the following equation (2):
                                                                        ∂                2                            ⁢              θ                                      ∂                              t                2                                              -                                    V              p              2                        ⁢                                          ∇                2                            ⁢              θ                                      =                                                                              ∂                  2                                ⁢                θ                                            ∂                                  t                  2                                                      -                                                            λ                  +                                      2                    ⁢                    μ                                                  ρ                            ⁢                                                ∇                  2                                ⁢                θ                                              =                      div            ⁢                                                  ⁢                          F              →                                                          (        2        )            
wherein, div denote divergence, and Vp denotes pressure wave propagation velocity.
Solving curl from the equation (1), to obtain the following equation (3):
                                                                        ∂                2                            ⁢                              w                →                                                    ∂                              t                2                                              -                                    V              s              2                        ⁢                                          ∇                2                            ⁢                              w                →                                                    =                                                                              ∂                  2                                ⁢                                  w                  →                                                            ∂                                  t                  2                                                      -                                          μ                ρ                            ⁢                                                ∇                  2                                ⁢                                  w                  →                                                              =                      rot            ⁢                                                  ⁢                          F              →                                                          (        3        )            
wherein, rot denotes curl. w=rot(U), Vs denotes pressure wave propagation velocity.
In traditional technology, detection of seismic wave merely refers to acquired of a projection of {right arrow over (U)}(t, x, y, z) on a vertical working direction of the wave detector, but not {right arrow over (U)}. Then various equations are derived according to the equation (2) to obtain the pressure wave; a projection of {right arrow over (U)}(t, x, y, z) in horizontal working direction of the detector is collected, then various equations are derived according to the equation (3) to obtain the shear wave. Joint solving and joint inversion are performed on the basis of these errors. Accordingly, the error is obvious.
As for the problem of big error in detection of full information of the seismic wave field in the prior art, there has not yet come up with an effective solution.